How can I change the size of the square of the camera which I see things through?
The render resolution in the render panel defines the upper limits in the dimensions of all renders through the camera, final or viewport.

You can also set a Render Border, using CtrlB in Object Mode, to restrict the rendered area in all views, (further restricted by the render resolution, when looking through the camera). In the 3D view, it's delineated with a red dashed frame.

In Object Mode, hitting  CtrlB again allows you to resize the border, and AltCtrlB dismisses it.